The Celtics were looking to cash in with three first-round picks (Nos. 15, 24, 25), using them to retool a team that had sneaked into the playoffs with 36 wins.

They used the 15th pick on Al Jefferson, a player with easily apparent upside. At No. 24 they took Delonte West, followed by Tony Allen, two players they had targeted all along, Celtics president of basketball operations Danny Ainge said at the time.

Coach Doc Rivers threw both guards into the mix quickly. West played 39 games; Allen played 77 and started 34.

“We needed them to step in and play a role right out of the gate,’’ Ainge said.

The Celtics find themselves picking at No. 25 again Thursday. But this isn’t the 2004 draft class, and the Celtics aren’t retooling. Ainge has done his due diligence, poring over film, watching workouts across the country, working the phones to gauge interest for a late-round pick. He’s realistic about how much of an impact a rookie can have on such a veteran team.

“I think every year is different,’’ Ainge said. “There have been years where we draft at 25 and we have great excitement and high expectations. Then, there’s years we’ve drafted at a similar number and we weren’t as excited and didn’t have a clear picture. Sometimes there are players that stand out that make it much easier.

“But the reality is, at 25, for that player to have a major impact in the NBA, it’s not a high percentage. It’s roughly 10 percent. But we always feel going into the draft that we have to do well. We have to do better than what the odds say and we have to find somebody that can contribute to our team.’’

Last year, the Celtics took Avery Bradley at 19. Bradley is the only Celtics draft pick from the past three years still on the roster. The rest barely left fingerprints.

J.R. Giddens was the first-round pick in 2008, at No. 30. He played in six games as a rookie, and 21 in his second season before being traded to New York along with Bill Walker (the second-round pick in 2008) and Eddie House. Walker is still with the Knicks. Giddens was last seen playing in Poland.

“Every year’s different, every player’s different, every team’s different,’’ Ainge said. “So there’s no set plan. It depends on who the player is, it depends on how ready he is. It depends on what our team is like and what opportunities may come. Every year’s different. So we may draft a player because he’s the best player, but we may be overloaded at that position. That player may have to wait his turn.’’

Since the 2000 draft, nearly 30 percent of the players taken between picks 10 and 30 are out of the league. This year’s draft class is notably low on star power and shallow overall.

“I don’t think it’s a great draft,’’ Ainge said. “But I’m hopeful that we can find somebody that can help us.’’

To that end, Ainge considers Bradley, who played 30 games as a rookie, more like his first-round pick this season.

“Avery’s situation was obviously different because we knew when we drafted him that he was hurt,’’ Ainge said. “We knew that he was 19 years old and had never played point guard, so we sort of knew that Avery was going to be our this year’s first-round pick more than he was our last year’s first-round pick.’’

Ainge said he’s considering trading the 25th pick. The Celtics also own the 55th selection.

“I’m always looking at those options,’’ he said. “But it depends what I can move it for. We’re always exploring those options and we have been probably more diligent this year than we have in years past.’’